I have posted recently on drawing, particularly on drawing as a form of thinking (here, here and here). I have now just read Patricia Cain’s superb new book on this topic, Drawing: The Enactive Evolution of the Practitioner. The author is an artist, and the book is based on her PhD thesis. She set out to understand the thinking processes used by two drawing artists, by copying their drawings. The result is a fascinating and deeply intelligent reflection on the nature of the cognitive processes (aka thinking) that take place when drawing. By copying the drawings of others, and particularly by copying their precise methods and movements, Dr Cain re-enacted their thinking. It is not for nothing that drawing has long been taught by having students copy the works of their teachers and masters – or that jazz musicians transcribe others’ solos, and students of musical composition re-figure the fugues of Bach. This is also why pure mathematicians work through famous or interesting proofs for theorems they know to be true, and why trainee software engineers reproduce the working code of others: re-enactment by the copier results in replication of the thinking of the original enactor.

In a previous post I remarked that a drawing of a tree is certainly not itself a tree, and not even a direct, two-dimensional representation of a tree, but a two-dimensional hand-processed manifestation of a visually-processed mental manifestation of a tree. Indeed, perhaps not even always this: A drawing of a tree is in fact a two-dimensional representation of the process of manifesting through hand-drawing a mental representation of a tree.

After reading Cain’s book, I realize that one could represent the process of representational drawing as a sequence of transformations, from real object, through to output image (“the drawing”), as follows (click on the image to enlarge it):

It is important to realize that the entities represented by the six boxes here are of different types. Entity #1 is some object or scene in the real physical world, and entity #6 is a drawing in the real physical world. Entities #2 and #3 are mental representations (or models) of things in the real physical world, internal to the mind of the artist. Both these are abstractions; for example, the visual model of the artist of the object may emphasize some aspects and not others, and the intended drawing may do the same. The artist may see the colours of the object, but draw only in black and white, for instance.

Entity #4 is a program, a collection of representations of atomic hand movements, which movements undertaken correctly and in the intended order, are expected to yield entity #6, the resulting drawing. Entity #4 is called a plan in Artificial Intelligence, a major part of which is concerned with the automated generation and execution of such programs. Entity #5 is a label given to the process of actually executing the plan of #4, in other words, doing the drawing.

Of course, this model is itself a simplified idealization of the transformations involved. Drawing is almost never a linear process, and the partially-realized drawings in #6 serve as continuing feedback to the artist to modify each of the other components, from #2 onwards.